Ok, first let me say I know very little about audio. I know how to operate the cameras and shoot, but when it comes to Audio, forget it.

So here is my question.
I own a Canon XH-A1. Im looking for an external Mic for it. I know there are many types and you can spend thousands. Im looking to spend a few hundred. Im looking for a Shotgun Mic, but its hard if not impossible to find one that says its Stereo.

So, lets take the Rode NTG-2 for example. Its not Stereo, right? But what if you split the XLR out of the Mic and ran it into both XLR's on the Camera. Is that possible? Is there any advantage in doing this?

What are you planning to use it to record? That affects the stereo/mono question - stereo is often used for music and ambience but most dialog is recorded in mono.

Splitting the mic to both channels doesn't produce stereo, it produces dual-mono. Not a bad thing because if your camera allows each channel to be set to its own level you can record one channel 6-8db lower than the other, providing insurance that if a sudden loud drive the main channel into overload, the other lower level channel is there as a backup.